Hi.
Basically, ibuprofen (Advil) is more potent than acetaminophen (Tylenol) in treating pain. However, acetaminophen is relatively safer to take than ibuprofen as it has fewer and milder side-effects, especially gastrointestinal side-effects.
For back pain, which is usually caused by conditions associated with inflammation, ibuprofen might be the better choice. For headaches, it would be best to try acetaminophen first before moving up to ibuprofen when pain does not resolve.
Hope this answers your query.
As a non-Doctor....
Advil for back pain- it has anti-inflammatory properties which can help with the pain- does not cure back pain.
For headaches, I like Excedrin Maximum, which is Tylenol+Aspirin+Caffeine.
No side effects if used as recommended and not abused.